(I) (I) Microturbulence in magnetic fusion devices –Microturbulence in magnetic fusion devices –New insights from gyrokinetic simulation & theoryNew insights from gyrokinetic simulation & theory

F. JenkoF. Jenko, C. Angioni, T. Dannert, F. Merz, A.G. Peeters, and P. Xanthopoulos, C. Angioni, T. Dannert, F. Merz, A.G. Peeters, and P. Xanthopoulos

IPP, Garching and GreifswaldIPP, Garching and Greifswald

(II) (II) Theoretical understanding ofTheoretical understanding ofcore transport phenomena in ASDEX Upgradecore transport phenomena in ASDEX Upgrade

C. AngioniC. Angioni, R. Dux, A. Manini, A.G. Peeters, F. Ryter, R. Bilato, T. Dannert,, R. Dux, A. Manini, A.G. Peeters, F. Ryter, R. Bilato, T. Dannert,A. Jacchia, F. Jenko, C.F. Maggi, R. Neu, T. Pütterich, J. Schirmer,A. Jacchia, F. Jenko, C.F. Maggi, R. Neu, T. Pütterich, J. Schirmer,J. Stober, W. Suttrop, G. Tardini, and the ASDEX Upgrade teamJ. Stober, W. Suttrop, G. Tardini, and the ASDEX Upgrade team

IPP, GarchingIPP, Garching

2121stst IAEA Fusion Energy Conference, Chengdu/China, 16-21 October 2006 IAEA Fusion Energy Conference, Chengdu/China, 16-21 October 2006

ComplexComplexphphenomenaenomena

Quasilinear modelsQuasilinear models Nonlinear gyrokineticNonlinear gyrokineticsimulationssimulations

All nonlinear gyrokinetic simulations shown in this talkAll nonlinear gyrokinetic simulations shown in this talk

have been performed with the continuum code have been performed with the continuum code GENEGENE..

A rough outline of this talkA rough outline of this talk

PART IPART I

PART

II

PART

II

Adiabatic ITG turbulence in a simple tokamakAdiabatic ITG turbulence in a simple tokamak

Reference case for core turbulence simulations:Reference case for core turbulence simulations:

• “ “Cyclone base case” – also serves as standard paradigm of turbulenceCyclone base case” – also serves as standard paradigm of turbulence• idealized physical parameters; adiabatic electrons; s-idealized physical parameters; adiabatic electrons; s-αα model equilibrium model equilibrium

Key findings:Key findings:

• saturation via zonal flowssaturation via zonal flows• ion heat flux is offset-linearion heat flux is offset-linear• nonlinear upshift of thresholdnonlinear upshift of threshold

GENE data

What about all the other transport channels?What about all the other transport channels?

How generic is the adiabatic ITG s-How generic is the adiabatic ITG s-αα scenario? scenario?

Microturbulence in stellaratorsMicroturbulence in stellarators

An example: Wendelstein 7-XAn example: Wendelstein 7-X

N>100 parallel grid N>100 parallel grid pointspoints

Field-aligned, Clebsch-type coordinatesField-aligned, Clebsch-type coordinates[Xanthopoulos and Jenko, PoP 2006].[Xanthopoulos and Jenko, PoP 2006]. Still: Still:

W7-X is minimized with respect toW7-X is minimized with respect toneoclassical losses:neoclassical losses:

Role of turbulent transport inRole of turbulent transport in(optimized) stellarators?(optimized) stellarators?

Effect of magnetic geometry onEffect of magnetic geometry onturbulence (tokamak edge etc.)?turbulence (tokamak edge etc.)?

A A = = R/a > 10R/a > 10

Adiabatic ITG turbulence in the stellarator Adiabatic ITG turbulence in the stellarator W7-XW7-X

Nonlinear upshiftNonlinear upshift of critical temperature gradient by some 20%. of critical temperature gradient by some 20%.

Very low transport levelsVery low transport levels due to strong zonal flow activity ( due to strong zonal flow activity (ωωEE»»γγ).).

linear threshold:linear threshold:R/LR/LTiTi ≈ 9 ≈ 9

(a/L(a/LTiTi ≈ 1) ≈ 1)

increasing R/LTi

TEM turbulence in tokamaksTEM turbulence in tokamaks

w/ ZFsw/ ZFs w/ow/oZFsZFs

Basic properties of TEM turbulenceBasic properties of TEM turbulence

Systematic gyrokinetic study of TEM turbulence:Systematic gyrokinetic study of TEM turbulence:

1.1. Relatively weak zonal flow activityRelatively weak zonal flow activity

2.2. Formation of radial structuresFormation of radial structures

3.3. Structures appear to be remnants of linear modesStructures appear to be remnants of linear modes

[Dann

ert &

Jenko

‘05]

[Dann

ert &

Jenko

‘05]

Φ Φ vs.vs. n ntt Φ Φ vs.vs. n npp Φ Φ vs.vs. T T Φ Φ vs.vs. T T

αα αα αα αα

kk yy

Nonlinear saturation in TEM turbulenceNonlinear saturation in TEM turbulence

For the transport-dominating modes, the For the transport-dominating modes, the ExB nonlinearityExB nonlinearity is well represented by a is well represented by a

diffusivitydiffusivity::

transportdominating

regime

transportdominating

regime

Nonlinear saturation in TEM turbulence Nonlinear saturation in TEM turbulence (cont’d)(cont’d)

Dressed test mode approachDressed test mode approach in the spirit of renormalized in the spirit of renormalized perturbation theory explains nonlinear saturation and serves as perturbation theory explains nonlinear saturation and serves as

basis for a basis for a transport modeltransport model..

Dressed test mode Dressed test mode approach:approach:

Parallel weighting:Parallel weighting:

weighting function

A novel quasilinear transport modelA novel quasilinear transport model

weighted w.r.t. parallel mode structureweighted w.r.t. parallel mode structure

QQii and and ΓΓ from QL ratios from QL ratios

This model is able to capture key features of TEM turbulenceThis model is able to capture key features of TEM turbulenceand can be used to predict TEM-induced transport.and can be used to predict TEM-induced transport.

QL modelQL modelNL GK simulationNL GK simulation

An empirical critical gradient modelAn empirical critical gradient model

• Many dedicated experiments with Many dedicated experiments with dominant electron heatingdominant electron heating

• Transport is dominated by Transport is dominated by TEM turbulenceTEM turbulence (low T (low Tii →→ ETG modes stable) ETG modes stable)

• Interpretation via an Interpretation via an empirical critical gradient (CG) modelempirical critical gradient (CG) model::

• Confirmed by Confirmed by nonlinear gyrokinetic simulations with GENEnonlinear gyrokinetic simulations with GENE::

R/Ln = 0

[F. Imbeaux et al., PPCF 2001][F. Imbeaux et al., PPCF 2001][X. Garbet et al., PPCF 2004][X. Garbet et al., PPCF 2004]

R/LR/Lnn > 2.5 > 2.5

Conventional (quasi-)linear models:Conventional (quasi-)linear models:no critical gradient no critical gradient (density gradient drive)(density gradient drive)

Nonlinear simulations and new quasilinear model:Nonlinear simulations and new quasilinear model:effective critical gradienteffective critical gradientelectron heat fluxelectron heat flux has has offset-linearoffset-linear scaling scaling

R/LR/LTe Te dependence for ‘large’ density dependence for ‘large’ density gradientsgradients

• similar as in adiabatic ITG casesimilar as in adiabatic ITG case• implies Timplies Tee profile stiffness profile stiffness• coupling of particle and electron heat fluxcoupling of particle and electron heat fluxe

lect

ron/ion h

eat

flux

GENEvs.QL model

qq dependence of TEM-induced dependence of TEM-induced transporttransport

Conventional QL theories predict a relatively weak dependence on Conventional QL theories predict a relatively weak dependence on qq, but:, but:

simulationsimulation

resultsresults

[Jenko

& D

annert ‘0

5]

[Jenko

& D

annert ‘0

5]

modelmodelEddy size (kEddy size (kyy))scales with scales with q q

Part of the Part of the qq scaling is provided by the scaling is provided by the qq dependence of the threshold: dependence of the threshold:

GK/QL(GS2)

GF/QL(GLF23)

TEP theory(Isichenkoet al. 1995)

Nonlinear and quasilinear gyrokinetics show good agreementNonlinear and quasilinear gyrokinetics show good agreement, while both, while boththe GF model and TEP theory predict smaller values of the marginal R/Lthe GF model and TEP theory predict smaller values of the marginal R/Lnn..

Main reason: Main reason: Model adjusts kModel adjusts kyy value, and transition point depends on k value, and transition point depends on kyy..

States of zero particle flux in ITG-TEM States of zero particle flux in ITG-TEM turbulenceturbulence

Observation of a particleObservation of a particlepinch (Γ < 0) for low valuespinch (Γ < 0) for low valuesof R/Lof R/Lnn (ITG regime). (ITG regime).

[Jenko, Dannert & Angioni ‘05]

ν = β = 0

Experimental identification of TEM featuresExperimental identification of TEM features

• AUG L-mode plasmasAUG L-mode plasmas

[0.8 MW ECRH, little OH)[0.8 MW ECRH, little OH)• gradual reduction of gradual reduction of

central ECRH, balanced by central ECRH, balanced by increaseincrease

of off-axis heatingof off-axis heating

2i

e

T

T

Existence of a threshold in R/LExistence of a threshold in R/LTeTe

[F. Ryter et al., PRL [F. Ryter et al., PRL 2005]2005]

ETG stable

Threshold behavior is observed directly; Threshold behavior is observed directly; power balancepower balance and and transienttransient

transporttransport consistent with both consistent with both linear gyrokineticslinear gyrokinetics and and CG modelCG model..

Collisional stabilization of TEMsCollisional stabilization of TEMs

Density ramp in AUG L-mode plasmas and quasilinear analysisDensity ramp in AUG L-mode plasmas and quasilinear analysis

With increasing collisionality, the R/LWith increasing collisionality, the R/LTeTe dependence of the electron heat dependence of the electron heat

flux decreases. Eventually, the dominant mode changes from TEM to ITG.flux decreases. Eventually, the dominant mode changes from TEM to ITG.

Impurity transport in the coreImpurity transport in the core

Experimental observations in AUGExperimental observations in AUG

General finding:General finding:

No central impurity accumulation whenNo central impurity accumulation whencentral heat transport is anomalous!central heat transport is anomalous!

Example:Example:

W accumulation is suppressed byW accumulation is suppressed by0.8 MW of central ECRH during a0.8 MW of central ECRH during ahigh density phase with 5 MW of NBIhigh density phase with 5 MW of NBI

[R. Neu et al., JNM 2003]

Quasilinear gyrokinetic study of an impurity Quasilinear gyrokinetic study of an impurity tracetrace

R /

LR

/ L

nn =

-R

V /

D =

-R

V /

D

A = 2 ZA = 2 Z

#15524 (ECRH phase; mid radius)

In confinement region, impurity transport is likely to be turbulentIn confinement region, impurity transport is likely to be turbulent..

High-Z limit is well behaved – in contrast to neoclassical theory.High-Z limit is well behaved – in contrast to neoclassical theory.

nominal parameters & R/Lnominal parameters & R/LTzTz=R/L=R/LTiTi (ITG) (ITG)

R/LR/LTeTe & collisionality & collisionality (TEM) (TEM)

W ionization stage (Z=46, A=184; ITG)W ionization stage (Z=46, A=184; ITG)

Momentum and ion heat transportMomentum and ion heat transport

Effects of electron heating on ion heat Effects of electron heating on ion heat transporttransport

• In In very low densityvery low density H-mode plasmas, one finds a strong H-mode plasmas, one finds a strongconfinement degradationconfinement degradation in response to in response to central ECRHcentral ECRH

• Related R/LRelated R/LTiTi drop due to drop due to increase of Te/Tiincrease of Te/Ti (implies reduction (implies reductionof ITG threshold) of ITG threshold) andand reduction of vreduction of vtortor (decrease of (decrease of ωωEE))

[A. Manini et al., NF submitted]

Coupling of momentum and ion heat Coupling of momentum and ion heat transporttransport

• Strong correlation betweenStrong correlation betweenTTii and and vvtortor

• Consistent with constant Consistent with constant ratioratio

of of χχΦΦ / / χχii

• Power balance analysis Power balance analysis (ASTRA,(ASTRA,

FAFNER, TRANSP, TORIC) FAFNER, TRANSP, TORIC)

yieldsyieldsa ratio of ~ 1 at mid a ratio of ~ 1 at mid

radiusradius

• Promising agreement with Promising agreement with bothboth

quasilinear and quasilinear and nonlinearnonlinear

GK studies of ITG GK studies of ITG modesmodes

[A. Peeters et al., PoP ’05 & PPCF submitted]

Insights and conclusionsInsights and conclusionsSpecific insights:Specific insights:

• The adiabatic ITG paradigm is not universal (see, e.g., The adiabatic ITG paradigm is not universal (see, e.g.,

TEM)TEM)

• QL models can be quite successful when used with QL models can be quite successful when used with

carecare

• Experimental TEM studies can be related to NL Experimental TEM studies can be related to NL

gyrokineticsgyrokinetics

• Different transport channels tend to be strongly Different transport channels tend to be strongly

coupledcoupled

General conclusions:General conclusions:

• No real predictive capability without deeper No real predictive capability without deeper

understandingunderstanding

• There is room for more synergy between theory, There is room for more synergy between theory,

modelling, modelling, and experimentand experiment

See posters: EX / 8-5Ra & EX / 8-5RbSee posters: EX / 8-5Ra & EX / 8-5Rb